Question

Solve :
$\frac{dy}{dx}+y\cot x=2x+x^2$

Answer 1

Given,

$\frac{dy}{dx}+y\cot x=2x+x^2$

$\frac{dy}{dx}=2x+x^2-y\cot x$

integrating on both sides, we get,

$y+c=x^2+\frac{x^3}{3}-y\ln |\sin x|+c$

$y+y\ln |\sin x|=x^2+\frac{x^3}{3}$

$y(1+\ln |\sin x|)=x^2+\frac{x^3}{3}$